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Lie symmetry analysis, Bäcklund transformations, and exact solutions of a (2 + 1)-dimensional Boiti-Leon-Pempinelli system. (English) Zbl 1385.37079
The Lie point symmetries of the (2+1)-dimensional Boiti-Leon-Pempinelli system are determined. There is an infinite family of symmetry generators which reduces to seven elements by appropriate choices of the arbitrary functions appearing in the generators. The Lie algebra is then seven-dimensional and an optimal system of one-dimensional subalgebras is constructed. Symmetry reductions and group invariant solutions are given. The truncated Painlevé analysis is used to find the Bäcklund transformation and the lump-type solutions are derived. The fusion-type $$N$$-solitary wave solutions are also obtained. Moreover, it is shown that this system is integrable in terms of a consistent Riccati expansion.

##### MSC:
 37K05 Hamiltonian structures, symmetries, variational principles, conservation laws (MSC2010) 37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) 37K35 Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems 35Q53 KdV equations (Korteweg-de Vries equations) 35B06 Symmetries, invariants, etc. in context of PDEs 76M60 Symmetry analysis, Lie group and Lie algebra methods applied to problems in fluid mechanics
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